Kinetic molecular theory

IB Chemistry HL· 30 min read

1. Core Postulates of KMT★★☆☆☆⏱ 10 min

Kinetic molecular theory is a microscopic model that describes the behavior of ideal gases, built on 5 core testable postulates about gas molecules and their motion.

📘 Definition

Ideal gas

A hypothetical gas that follows all KMT postulates exactly. Most real gases behave nearly ideally at low pressure and high temperature.

Example:

Nitrogen gas at 1 atm and 25°C approximates ideal behavior very closely.

Gases consist of large numbers of tiny particles, far apart relative to their own size: most volume of a gas is empty space, so molecular volume is negligible.
Gas molecules move constantly in random, straight-line motion, colliding frequently with each other and container walls.
All collisions are elastic: total kinetic energy is conserved, no net energy loss over time.
There are no attractive or repulsive intermolecular forces between ideal gas molecules.
The average kinetic energy of gas molecules is directly proportional to the absolute temperature of the sample.

📐 Worked Example

Which of the following is NOT a postulate of KMT for ideal gases? A) Collisions between gas molecules are elastic B) The volume of gas molecules is negligible compared to total volume C) Intermolecular forces between molecules are significant D) Average kinetic energy is proportional to absolute temperature

1
Recall the 5 core postulates of KMT. One key postulate explicitly states that there are no attractive or repulsive forces between ideal gas molecules.
2
Evaluate the options: Option C directly contradicts this postulate, so it is not a postulate of KMT.
3
Answer: C

Exam tip:

You can be asked to state KMT postulates for 2-3 marks in Paper 2, so memorize all five clearly.

2. Linking KMT to Macroscopic Gas Properties★★★☆☆⏱ 15 min

KMT explains why empirical gas laws work by connecting microscopic molecular behavior to the macroscopic properties we measure experimentally.

📘 Definition

Gas pressure

The force per unit area exerted by gas molecules colliding with the walls of their container.

For example, Boyle's law ( $P \propto 1/ V$ at constant $T$ ) is explained by KMT: decreasing volume increases the number of collisions per unit area of container wall, increasing pressure. Similarly, increasing temperature increases average molecular speed, leading to more forceful collisions and higher pressure at fixed volume (Gay-Lussac's law).

📐 Worked Example

Use kinetic molecular theory to explain why the pressure of a gas in a sealed fixed-volume container increases when temperature increases.

1
From KMT postulates, absolute temperature of a gas is directly proportional to the average kinetic energy of its molecules.
2
When temperature increases, average kinetic energy increases, so molecules move faster on average.
3
Faster molecules collide with the container walls more frequently and with greater force per collision. Since volume is fixed, the total force per unit area (pressure) increases.

3. Kinetic Energy and Molecular Speed★★★★☆⏱ 15 min

A key mathematical result derived from KMT gives the relationship between temperature, molar mass, and average molecular speed. The core derivation leads to:

\frac{1}{2}Nm\overline{c^2} = \frac{3}{2}nRT

Rearranging gives the root mean square speed, the most common measure of average molecular speed:

v_{rms} = \sqrt{\frac{3RT}{M}}

Where $R$ is the gas constant ( $8.31 J K^{- 1} mol^{- 1}$ ), $T$ is absolute temperature in Kelvin, and $M$ is molar mass in $kg mol^{- 1}$ . This result shows that at the same temperature, lighter gases have higher average molecular speed than heavier gases.

📐 Worked Example

Calculate the root mean square speed of oxygen ( $O_{2}$ ) molecules at 27°C, given $R = 8.31 J K^{- 1} mol^{- 1}$ , molar mass of $O_{2} = 32.00 g mol^{- 1}$ .

1
Convert temperature to Kelvin and molar mass to $kg mol^{- 1}$ to match the units of $R$ :
2
$T = 27 + 273 = 300 \text{ K}, \quad M = 32.00 \text{ g mol}^{-1} = 0.03200 \text{ kg mol}^{-1}$
3
Substitute into the $v_{r m s}$ formula:
4
$v_{rms} = \sqrt{\frac{3 \times 8.31 \times 300}{0.03200}} = \sqrt{233718.75}$
5
Calculate the final result:
6
$v_{rms} \approx 480 \text{ m s}^{-1}$

Exam tip:

Always check units: forgetting to convert molar mass from g to kg is a common exam mistake.

4. Deviation of Real Gases from Ideal Behavior★★★★☆⏱ 15 min

No real gas follows KMT postulates exactly, because two core assumptions are only approximately true at low pressure and high temperature:

Molecular volume is not always negligible: at high pressure, molecules are crowded close together, so their own volume makes up a significant fraction of total volume.
Intermolecular forces are not zero: at low temperature, molecules move slowly enough that intermolecular attractions affect their motion.

📘 Definition

Compressibility factor

Z

A measure of deviation from ideal behavior, defined as $Z = \frac{P V}{n R T}$ . $Z = 1$ for ideal gases.

📐 Worked Example

Use KMT to explain why carbon dioxide deviates more from ideal behavior at 0°C than at 100°C, at the same pressure.

1
At lower temperature, gas molecules have lower average kinetic energy, so they move slower.
2
Slower molecular motion allows intermolecular attractive forces, which KMT assumes to be zero for ideal gases, to have a significant effect on molecular motion.
3
At 100°C, higher average kinetic energy overcomes intermolecular attractions, so behavior is much closer to ideal. At 0°C, intermolecular forces are significant, so deviation is larger.

5. Common Pitfalls

Wrong move:

Forgetting to convert molar mass from g mol⁻¹ to kg mol⁻¹ when calculating $v_{r m s}$

Why:

The gas constant $R = 8.31$ J K⁻¹ mol⁻¹ has units of kg m² s⁻², so incorrect units give a result ~30x smaller than the correct value

Correct move:

Always convert molar mass to kg mol⁻¹ before substituting into the $v_{r m s}$ formula

Wrong move:

Claiming all individual gas molecules have the same speed at a given temperature

Why:

KMT states that average kinetic energy (not individual molecular speed) is proportional to temperature. There is a wide distribution of molecular speeds in any sample.

Correct move:

KMT describes average behavior of a large collection of molecules, not the speed of any single molecule

Wrong move:

Stating that only heavy gases deviate from ideal behavior

Why:

All real gases deviate from ideal behavior under appropriate conditions, regardless of molar mass

Correct move:

Deviation increases with stronger intermolecular forces and higher molar mass, but all real gases deviate from ideal behavior at high pressure/low temperature

Wrong move:

Mix up the conditions for maximum deviation: claiming high temperature/low pressure causes maximum deviation

Why:

These are the conditions where real gases are closest to ideal, because molecular volume is negligible and intermolecular forces are weak

Correct move:

Maximum deviation from ideal behavior occurs at high pressure and low temperature

6. Quick Reference Cheatsheet

Concept	Key Result	Notes for Exam
Ideal gas KMT postulates	Elastic collisions, no IMFs, negligible molecular volume, random motion, $\overline{K E} \propto T$	Memorize all 5 for explanation questions
Root mean square speed	$v_{r m s} = \frac{3 R T}{M}$	Convert M to kg mol⁻¹, T to Kelvin, use R = 8.31 J K⁻¹ mol⁻¹
C	o	n	d	i	t	i	o	n	s		f	o	r		i	d	e	a	l		b	e	h	a	v	i	o	r
L	o	w		p	r	e	s	s	u	r	e	,		h	i	g	h		t	e	m	p	e	r	a	t	u	r	e
M	o	l	e	c	u	l	e	s		f	a	r		a	p	a	r	t	,		h	i	g	h		K	E		o	v	e	r	c	o	m	e	s	I	M	F	s

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2025 · P1
Identify non-KMT postulate
2024 · P2
Calculate rms speed
2023 · P1
Explain real gas deviation

What's Next

Kinetic molecular theory is the foundational microscopic model for gas behavior in IB Chemistry HL, connecting molecular motion to measurable macroscopic properties of gases. It also sets the stage for understanding why real gases deviate from ideal behavior, which depends directly on the strength of intermolecular interactions between molecules. KMT's core relationship between absolute temperature and average molecular kinetic energy also underpins key concepts in later topics, including thermochemistry (energy transfers between systems) and reaction kinetics (the effect of temperature on reaction rate). Mastering KMT is critical for answering both calculation and explanation questions across multiple units of the IB Chemistry HL syllabus.